Let X be a random variable with mean 6 and variance 3. Let Y be the random variable counting the number of times the number 1 appears when rolling six fair four-sided dice. Assume that X and Y are independent. Define Z to be the random variable 2X − 3Y + 1. Find E(Z).

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Q: national mean of 11%? Use a = 0.01. (a) What is the level of significance? State the null and…

A: Sample size n = 16 Sample mean = 12.9 Population SD = 5

Q: If the variances for independent random variables X and Y is Var(X)=0.15 and Var(Y)=5.62 then Var…

A: Given that  Var(X)=0.15 Var(Y)=5.62

Q: random variable X is an of X is 6, determin

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Q: If X is normal random variable with mean 3 and variance 5, then find the probability P(2 < X <6).

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Q: Suppose that X is a N(3,4) random variable and suppose that Y=2X+3. Determine P(Y>11.4).

A: We have given that,  Let X be the random variable from N(3, 4) and Y = 2X + 3  Then,  We will find…

Q: Suppose Y is a discrete random variable with the following probability distribution: P(Y = 1) = 0.25…

A: Introduction In statistics, a discrete random variable is a random variable that can take on a…

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A: Step 1: Given that x follows binomial distribution with mean 6 and variance =4.2 That is,…

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A: It is given thatE(X)=μXVar(X)=σX2

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A: Given that  E(X)=3    , E(Y)=2    , Var(X)=2   , Var(Y)=4 X and Y are independent then…

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A: f(x)=

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Q: If the variance of the discrete random variable X = 36

A: Variance is 36

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A:

Q: Let X be a random variable with a mean of 50 and a variance of 64. Find: i. P(x< 52) ii. P(35 < X <…

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Q: Suppose that the number of accidents occurring on a highway each day is a Poisson  random variable…

A: Givenλ=3.1 for each dayLet "x" be the no.of accidents occur in a dayx~Poisson(λ=3.1)P(X=x)=e-λ×λxx!…

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A: Here Given  Pair of dice are rolled  So Total Possible number of Outcome=6×6=36

Q: If the random variable ?takes the values 1, 2, 3, 4 such that 3P(X=1)= 4P(X=2 )= P(X=3) = 5P(X=4).…

A: It is given that, 3P(X=1)= 4P(X=2 )= P(X=3) = 5P(X=4)

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A: 0.070Explanation:Step 1:  correlation coefficient  between X and Y is given by…

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A: B) 3/4

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A: Given: n=7 and p=0.1 Then, the variance isVariance=np1-p=70.11-0.1=70.10.9=0.63

Q: Let X and Y and Z are uncorrelated random variables with the same variance. Find the correlation…

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Q: Let X be a binomial random variable with parameters n = 20 and p ( p is intentionally not given in…

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Q: Suppose that X is a N(3,4) random variable and suppose that Y=2X-1. Determine P(Y>8).

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A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: 2. Let the mgf of a random variable X be Find P(X 1 or X 2).

A: We want to find the P(X=1 or X=2)

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A: For a Discrete Random Variable X where X takes only three values that is 0,2 and 3 P(0)=0.5 ,…

Q: (a) What is the level of significance? State the null and alternate hypotheses. Will you use a…

A: Sample size n = 7 Population SD = 4.75 Sample mean = (32+26+42+36+30+35+30)/7 = 33

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A: Let X be a random variable with the values a and b. The probability distribution table is…